Triangle Area
A = √(s(s-a)(s-b)(s-c))P = a+b+cThis calculator uses Heron’s formula, which derives the area from the three sides without needing the height.
You compute the semi-perimeter — the sum of the sides divided by two — and the area is the square root of the semi-perimeter multiplied by its difference from each side.
The practical advantage is large: measuring three sides is easy with a tape, while measuring the height requires dropping a perpendicular from a vertex, which is rarely feasible in the field.
Not every combination of three measurements forms a triangle. The sum of any two sides must exceed the third.
Sides of 2, 3 and 10 do not close: the two shorter ones add to 5, not enough to reach the ends of the side of 10. The calculator therefore rejects the input rather than returning a meaningless number.
When the sum exactly equals the third side, the points fall on a line and the figure has zero area — a degenerate triangle.
The classic formula, base times height divided by two, remains valid and is more direct when you already have the height.
It is preferable in technical drawing and floor plans, where the height is usually dimensioned.
Heron’s formula is preferable for land measurement and any situation where only the edges are accessible.
Frequently asked questions
Because they violate the triangle inequality: the sum of two sides must exceed the third. Check for a typo or a mismatched unit.
No. Heron’s formula works from the three sides alone, which is what you can normally measure in practice.
Yes. Equilateral, isosceles or scalene — the formula makes no distinction, as long as the three sides form a valid triangle.
Split the area into triangles, calculate each and add them up. That is the technique used in surveying for irregular shapes.